HEAT FLUXES - and Equilibrium Temperatures

The giant planets receive, absorb and reflect sunlight - that's how we see
them (left picture). But they also emit heat - infrared light (right)

Integratingn over the whole disk, the spectrum of the whole disk has a "double
hump" - visible reflected sunlight at short wavelengths, and thermal IR
at longer wavelengths.

Knowing the total output of sunlight and that light decreases as 1/distance2,
we can calculate the amount of sunlight that should be hitting a square meter
of each planet. The ALBEDO (A) of a planet is the reflectivity of a planet.
Therefore, the total amount of sunlight absorbed the by the planet per square
meter is (1-A)x Solar Flux@Earth / distance2 (where distance from
the Sun is in AU). In equilibrium, we expect

ENERGY IN = ENERGY OUT

The energy emitted per square meter is described by the Stefan-Boltzmann
law for thermal emission: Power/Area = sigma x T4 where T = Temperature
of the radiating surface.

Allowing for the fact that objects receive an area 2piR2
of sunlight but emit from all 4piR2, and "normalizing" to the Earth
(at 1 AU), we get

Tequilibrium = 288K [(1-A)/a2]1/4

What happens when this equilibrium temperature is compared
with the TRUE temperature? How do we measure the TRUE temperature?

This figure (from Hubbard's chapter in The New Solar System) shows
that the giant planets tend to emit more energy than they receive - all except
Uranus where the internal heat source (red arrow) is negligible. Hartmann quotes
these ratios:

Jupiter

Saturn

Uranus

Neptune

Heat Emitted / Sunlight Absorbed

2.5

2.3

~1.1

2.7

This table tells us that all of the giant planets except Uranus emits about
21/2 times the amount of solar energy absorbed. What's
the story with Uranus? Why does it emit so much less energy? This is a MAJOR
issue of planetary science.

So, putting the IR thermal emission of these planets in context, how bright
do these giant planets glow? Is this really a lot of heat, like a star? If you
compare JSN with the Earth, they are BRIGHT - but they are pretty dim compared
with the Sun.

From Planets, Moons and Rings - ASTR 3750

INTERNAL HEAT SOURCES

The main source of heat comes from formation - gravitational collapse
and accretion of material

Gravitational Potential Energy -> Kinetic Energy (in-fall)
-> Heat

This happens very quickly - during formation.

Then, slowly material begins to settle downwards - DIFFERENTIATION. This process
is important for the Terrestrial Planets (more about that next week) but is
also important for the giant planets.

First consider Jupiter and Saturn - The energy release by the formation of
the small rock/iron cores is probably not very important for either Jupiter
or Saturn (the cores are so small). So, most of the heat coming from Jupiter
is thought to be primarily primordial - the heat generated in formation of the
planet. For Saturn we have a different story - 2 pieces of evidence (i) a depletion
of Helium in Saturn's atmosphere and (ii) lower internal temperatures on Saturn
(derived via internal models as per Class 11) - suggest that there is HELIUM
RAIN. That is, the PHASE DIAGRAM for H,He mixtures suggest that at high pressures
liquid helium does not mix with liquid hydrogen - just like oil and water. The
heavier liquid - helium - falls down through the hydrogen - the helium "rains
out". The slightly warmer temperatures inside Jupiter probably prevent
the helium from raining out much on Jupiter.

Second, what about Uranus and Neptune? These outer 2 giant planets are smaller
and denser - consistent with much more denser materials than hydrogen and helium.
We have discussed before that the prime candidates are the "hydrogen compounds"
(often called "ices" even though they are not solid as ices inside
the giant planets) which are made by combining the next most abundant elements
- oxygen, carbon and nitrogen - with the abundant hydrogen. These are WAM -
Water, Ammonia and Methane. These ices form the liquid layer outside the rock/metal
core, below the outermost layer of hydrogen & helium. If Uranus and Neptune
have similar interiors, why doesn't Uranus have a similar heat output? Was the
heat dissipated (e.g. stirred up in a giant impact) or is there a stable layer
of "opaque" material (a thermal blanket) preventing the heat from
escaping - while Neptune was stirred up by an impact?.......???????

FORMATION

First, the Astro 101 story - as the solar nebula cooled, refractory materials
condensed closer to the Sun while the more abundant, volatile "ices"
condensed outside the "frost line" (along with the less abundant rock
-> dirty snowballs).

The growing planet "embryos" were able to sweep up the surrounding
gas to become giant planets. All this happened VERY QUICKLY - within 1-10 million
years of the collapse of the original molecular cloud.

So - what about Uranus and Neptune? Farther out in the solar system the density
of the solar nebula was less and the collision times between accreting materials
is much slower. It is really difficult to make Uranus and Neptune where they
are currently located. It would be MUCH easier if we could make them closer
in and then allow them to migrate outwards. How can planets migrate? By interacting
(gravitationally - not necessarily colliding) with other objects - specifically,
Uranus and Neptune could migrate outwards by sending material inwards - where
the objects get kicked out by Jupiter. This is the current theory for the formation
of the Kuiper Belt - but wait a couple of months and there will probably be
another theory around......